So we both have torqshifts but mine has the awesome 6 speed automatic, while he is in the stone age with just 5 (haha). I believe my truck has the best of both worlds, but he won't shut up about 3.73 vs 3.55. I keep telling Him the gear ratios in the new tranny is why my 3.55 is superior.

20" wheels with 3.73 gears are basically the same overall ratio as an 18" rear with 3:55 rings.

All being equal, I would guarantee the lower ratio rears would be better in towing and economy.
His stock 6.4L will be as economical as an Abrams tank. On the other hand, if both trucks delete, there will be nothing you can do to match his power and economy, no matter which RR ratio you are running.

The Torqshift 5-speed 5R110 automatic transmission replaced the 4-speed in the 2003 model year truck with 6.0 L diesel engine. The TorqShift design in fact has six forward ratios, but only five are advertised, with the 'hidden' gear only used in extreme cold weather. The TorqShift 1st to 5th gear ratios are 3.11, 2.22, 1.55, 1.00, and 0.71:1. It also utilizes an alternate 4th gear, overdrive on 2nd gear of the 3-speed automatic component (0.72 x 1.55), that is 1.10:1 that is used under cold start conditions to aid engine and transmission warm up. On the TorqShift, once the Tow/Haul mode is activated it can help increase a driver's control when towing large loads up and down steep grades and automatically minimizes shifts and maximizes available torque. Upon descent, the Tow/Haul mode utilizes engine braking to help extend brake life and improve driver control. An adaptive shift function monitors the TorqShift's performance over its lifetime, and adjusts shift pressures in real time to assure consistent shift feel and compensate for wear. For ease of maintenance, the TorqShift's oil filter is a spin-off style, mounted on the passenger-side exterior of the transmission. Also the TorqShift's larger fluid lines and a larger transmission oil cooler help to assure cooler operating temperatures, even under the most demanding conditions. This was Ford's first automatic transmission to feature PTO. The transmission can be equipped with an integrated PTO provision (which automatically locks the torque converter providing power to the PTO gear when the operator turns on the PTO switch). .... Ford Super Duty - Wikipedia, the free encyclopedia

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